San Diego, California (CNN) -- A U.S. District Court judge declined Friday to release the findings from authorities' search of accused gunman Jared Lee Loughner's family home because a federal investigation is still ongoing and a grand jury is preparing an indictment.

Loughner, 22, is accused of shooting U.S. Rep. Gabrielle Giffords, D-Arizona, and 18 other people on January 8, six of them fatally.

An indictment could be ready by March 9, when two Arizona media outlets seeking the results of search warrants could renew their request, Judge Larry Burns said.

In another matter relating to Loughner, Burns said he would not make a ruling on a defense request to withhold two new mug shots of Loughner taken by the U.S. Marshals Service after his arrest in the mass shootings in Tucson, Arizona.

Loughner, who is being held by authorities in Arizona, did not appear in court Friday.

The marshals service attempt to release the two mug shots was based on a 6th Circuit Court ruling, and the judge said he would let media outlets in the 6th Circuit Court region -- Kentucky, Michigan, Ohio and Tennesse -- seek the release of the two mug shots.

Burns was assigned to the Loughner case by the 9th Circuit Court, where he's based, after Arizona federal judges recused themselves from the case because their state's chief federal judge was allegedly killed by Loughner. The 9th Circuit Court region includes California and Arizona.

Loughner's public defenders sought to bar the release of the mug shots after the U.S. Marshals Service planned to release them on February 7 under Freedom of Information Act requests made by 15 individuals, four of them within the 6th Circuit, according to court records and the judge.

But the judge commented that the mug shots of Loughner don't appear to jeopardize his right to a fair trial.

"I do not see a serious threat to his ability to get a fair trial if the two mug shots are released," Burns said.

Federal prosecutors and Loughner's public defender have opposed requests to make public the photos, asserting Loughner's privacy rights and his 6th Amendment guarantee for a fair trial.

The mug shot of a smirking Loughner that has widely appeared in the media was one taken by Pima County, Arizona, authorities after the shootings.

Federal prosecutors also opposed publicly disclosing the inventory of their search of Loughner's house after the shooting, arguing in court papers that the media doesn't have a right to search warrant materials until a formal indictment against Loughner is made.

But David Bodney, an attorney for two Arizona media outlets seeking the search warrant results, said federal officials have already released selective details of the search and added that the First Amendment and federal law provide "a strong presumptive right of public access" to the records.

But Bodney's arguments failed to convince the judge.

"I think his rulings were very understandable based on the information we heard for the first time ... namely there is still an investigation," Bodney said after Friday's hearing.

The publishing company for the Arizona Republic newspaper and the Phoenix television station KPNX Broadcasting Co. were seeking to make public the results -- or returns -- of at least two search warrants executed in the Loughner case, one issued by a Pima County judge on the day of the shootings and another issued January 12.

Loughner is accused of shooting Giffords in the head at a "Congress on Your Corner" event on January 8 at a Tucson grocery store and then shooting 18 other people, six of them fatally. The dead included Giffords staffer Gabe Zimmerman and U.S. District Judge John Roll. Giffords is recovering in a Houston rehabilitation hospital.

Loughner is charged with one count of attempting to assassinate Giffords and two counts of attempted murder in the shootings of Giffords staffers Pamela Simon and Ron Barber.

Loughner had also faced two murder charges in the deaths of Roll and Zimmerman, but in a procedural maneuver last week, prosecutors temporarily dropped those two charges and plan to bring them back under a superseding indictment that is expected to include other charges as well.

Prosecutors intend to present a superseding indictment containing the murder charges at the next status hearing in the case on March 9, said Robbie Sherwood, a spokesman for the U.S. attorney's office in Phoenix.

The federal government will prosecute Loughner before state prosecutors pursue a criminal case against him, federal and state prosecutors said this month.

Friday's hearing was held in San Diego because presiding Judge Burns and Loughner's federal public defender, Judy Clarke, are based in the city.

Burns is a 2003 Bush appointee serving in the U.S. District Court for Southern California in San Diego.

Last month, Burns entered not guilty pleas on behalf of Loughner, who declined to tell the court his plea during an arraignment. At that hearing, prosecutors said they had turned over hours of videos taken off Loughner's home computer to the defense.

Two federal judicial sources told CNN last month they expect Loughner's attorneys to ask that any trial be moved out of Arizona, possibly to San Diego, but the Justice Department indicated it would oppose a move.

The sources said they expect the defense to make a formal motion in coming weeks to move court proceedings to a neighboring jurisdiction because of pretrial publicity.

Earlier last month, federal sources said that whether to support an out-of-state change of venue, a move that has happened rarely in recent years, appeared to be an ongoing point of disagreement within the Justice Department. A trial also could be held in Arizona outside Tucson, those sources said. There are federal courthouses in Phoenix, Flagstaff and Yuma.

A final decision will be made by Roslyn Silver, the new chief judge of the federal courts in Arizona. The 1994 Clinton appointee to the federal bench has taken over for Roll.

Federal sources said Silver -- if asked to move the trial -- would consult with officials of the 9th Circuit, the federal judicial region that comprises nine Western states.